Robert C. Tautz

Plasma Instabilities

Plasma instabilities are a mechanism to convert free energy — for example a temperature anisotropy or directed particle motion — to electromagnetic field energy. While originally unwanted, because plasma instabilities can destroy the confinement in laboratory and fusion plasmas, nowadays such instabilities are used in astrophysics to model the generation of magnetic fields in initially unmagnetized plasmas. For example, the dissipation of kinetic energy even in collisionless plasmas can so be explained.

Transport Theory

Understanding the scattering processes of energetic charged particles — such as Cosmic Rays or Solar energetic particles — in turbulent electromagnetic fields is of paramount importance if one wants to understand observations on Earth. Although the basic problem is simple — describe the trajectory of a particle being deflected through the Lorentz force — the appropriate averaging over an ensemble to calculate meaningful diffusion coefficients has been a longstanding problem. However, by using non-linear theories and numerical test-particle simulations, significant progress has been made in the last years.

Kapteyn Series

Kapteyn series are infinite series of Bessel functions with the index of summation appearing in both the index and the argument of the Bessel functions involved. While they appear in many applications of theoretical physics and mathematics, such as radiation and optimization problems, the convergence of such series is, in general, unclear. Therefore, it is appropriate and necessary to undertake every effort of rewriting such sums in terms of, at worst, infinite power series or (double) integrals, the convergence of which can be estimated more reliably. More importantly, in many cases it has proven possible to find closed analytical expressions for Kapteyn series of both the first and the second kind. Such is indispensable for cases where Kapteyn series constitute only part of large mathematical expressions that have to be dealt with numerically.

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